Does this work?

If you put the numbers (x,y,z) = (2,1,1) your expression is zero. This means (x-y-z) could be a factor. By symmetry, (-x+y-z) and (-x-y+z) could also be factors. Last, (-2,1,1) also makes your expression zero. So (x+y+z) should be a factor. Try multiplying:

If you put the numbers (x,y,z) = (2,1,1) your expression is zero. This means (x-y-z) could be a factor. By symmetry, (-x+y-z) and (-x-y+z) could also be factors. Last, (-2,1,1) also makes your expression zero. So (x+y+z) should be a factor. Try multiplying: